A complete renormalization group trajectory between two fixed points

We will report our recent rigorous non-perturbative construction of a massless discrete trajectory for Wilson's exact renormalization group: we do not use hierarchical approximations. The model is a three dimensional Euclidean field theory with a modified free propagator. The trajectory realizes the mean field to critical crossover from the ultraviolet Gaussian fixed point to an analogy recently constructed by Brydges, Mitter and Scoppola of the Wilson-Fisher nontrivial fixed point.